A political analyst was curious if younger adults were becom

A political analyst was curious if younger adults were becoming more conservative. He decided to see if the mean age of registered Republicans was lower than that of registered Democrats. He selected a simple random sample of 128 registered Republicans from a list of registered Republicans and determined the mean age to be x139 years with a standard deviation of s1-8 years. He also selected an independent simple random sample of 200 registered Democrats from a list of registered Democrats and determined the mean age to be x 40 years with a standard deviation of s2 10 years. Let 1 and 2 represent the mean ages of the populations of all registered Republicans and Democrats respective Leto and 2 be the corresponding population standard deviations. Suppose it is reasonable to assume that the distributions of age in the populations of registered Republicans and of registered Democrats are Normal with the same standard deviation. Suppose the political analys had wished to test the hypotheses o versus A What a wes about the value of the P-value? 0.05

Solution

This is a one tailed z test, as there is enough sample size to approximate that (n > 30).

Getting the standard error of the difference,

sd = sqrt(s1^2/n1 + s2^2/n2)

Thus, sd = 1

As for a two sample diference z test,

z = (X1 - X2) / sd

Thus,

z = -1

which has a p value of, for a left tailed test,

p = 0.158655254

Thus, the answer is p-value > 0.10. [ANSWER, OPTION B]